A solution of the degenerate Neumann problem by the finite element method
M.I. Ivanov1, I.A. Kremer1,2, M.V. Urev1,2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk, Russia
2Novosibirsk State University, Novosibirsk, Russia
Keywords: вырожденная задача Неймана, условия согласования, ортогонализация правой части, конечные элементы, degenerate Neumann problem, matching conditions, orthogonalization of the right-hand side, finite elements
Abstract
This paper deals with the solution of the degenerate Neumann problem for the diffusion equation by the finite element method. First, an extended generalized formulation of the Neumann problem in the Sobolev space H1(Ω) is derived and investigated. Then a discrete analogue of this problem is formulated using standard finite element approximations of the space H1(Ω). An iterative method for solving the corresponding SLAE is proposed. Some examples of solving the model problems are used to discuss the numerical peculiarities of the algorithm proposed.
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